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  4. Four married couples are to be seated in a row having 8 chairs. The number of ways so that spouses are seated next to each other, is

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Q. Four married couples are to be seated in a row having 8 chairs. The number of ways so that spouses are seated next to each other, is

Permutations and Combinations

Solution:

Let us denote the four married couples of $C_1$, $C_2, C_3$ and $C_4$. We consider each couple as one unit. We can permute four units in 4 ! ways. Each couple can be seated in 2 ! ways. Thus, the required number of ways is
$(4 !)(2)(2)(2)(2)=384$.